Solars are Perfect at whatever skills they choose to develop and use. This doesn't make the job of the storyteller easy. Perfect in this case means a charm that allows them to avoid a roll entirely and say "I succeed". These include the perfect defenses, but would also include perfect attacks or a hypothetical Lore charm which instantly let you know all of a countries historic political weaknesses.

The essence of drama is conflict and conflict is only meaningful if there is a chance of failure. Perfects take away that chance of failure in the moment.

The Sidereals did manage to defeat the Solars by somehow orchestrating the most complex conspiracy possible. No GM should be forced to put in that much work just to get through one more session.

This is not an answer in itself, but conflict is not exclusively a matter of success or failure. It is better generalized into action and consequences. Put them into meaningful situations, where they have a choice between two things they want, but getting both is impossible. And make it a really, really painful choice.
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UndrerenNov 28 '12 at 16:33

Dragons, if in doubt add more dragons, has worked for me so far :)
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SkeithNov 28 '12 at 16:42

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@Undreren Expand that a bit more, and you have an answer. Please, expand on that a bit more :)
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Simon GillNov 28 '12 at 16:46

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Also, no matter how perfect they are, one big theme of the game is that scale is more important. Maybe you can perfectly soak an arrow, but how about 10 of them? 100? And even if you do soak all of it, what good does it do to your followers, who just took them all in the face?
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Cristol.GdMNov 28 '12 at 21:23

5 Answers
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While Solars are the most powerful exalt and can excel at what they choose to focus on, they always have flaws and weaknesses to exploit

Great Curse

The most obvious flaw a Solar possesses is the Great Curse, which is what causes them to turn into the biggest jerks in Creation eventually. There are tons of story elements that can be exploited by playing upon each player's great curse. It took me a while to realize that I should be handing out Limit like candy (and it's actually pretty easy to do so). Take for example a Solar who has a limit break, snaps, and murders a child. What are the consequences of that action? Certainly the mortals are not going to like them, and the wild hunt may be called out pretty quickly after that.

Virtues

Second among a Solar's flaws are their Virtues. If you have a virtue higher than 3, you must roll that virtue and fail in order to take the action you're attempting to do. Want to abandon that child and run after the bad guy? Compassion roll! Want to let the bad guy get away? Valor roll! Of course, they can use Willpower to take the action, but then they also get the precious precious limit.

Reliance on Perfect Defenses

Third would be the inability to reflexively use their defenses. Having the biggest most damage dealing combo in Creation is not going to save you if you didn't put your perfect defense into the combo. Because as soon as you pop your attack, you're going to take some kind of attack which you can't perfect out of the way of, because you used a charm. This is where we get the term Paranoia Combat.

Being awful at something you didn't focus on

"Did anyone take Sail?" - A Solar is great at what they choose to focus on. If they don't focus on something, they can get by better than a mortal, but they're still going to have issues. Put the Melee character into a social situation. Heck, throw in an Abyssal with some social charms and embarrass said character by introducing an unnatural mental compulsion to drop his pants in the center square.

Numbers, Numbers, Numbers

A single Solar is still a single Solar. At Essence 2, a well-prepared Dragon Blooded can take them out by themselves. Sure they might have a perfect defense to worry about, but they're going to slow-play the combat until the Solar is flaring to high-heaven and then stab their Jade Spear into the Anathema.

An arrogent Solar can even be taken out by Extras, especially if you can unexpected attack them. Remember that 6 attackers against 1 Defender means that 1 of the attacks per round will always be unexpected. The only perfect defense you can use against an unexpected attack (besides first making it expected) is the perfect soak, and that is hard to get off the bat.

Threaten something other than the Solar

Solars are supposed to be superheros. When you can't get directly at the hero, you target something they like. There aren't many charms that allow them to be in two places at once. Take something they care about, and threaten it. Threaten several things that they are attached to all at once. Destroy one of the things.

Give them Solar sized challenges

Like mentioned in the other answers, the Abyssals and Infernals are of the same power level as Solars. But, Yozis, 1st Circle Demons, the Neverborn, Unshaped Rhaksasa, and the like all have power levels even higher than that. You can also beef up NPCs with gear. Imagine an Infernal with the Cecylene tree that also has the Crown of Thunders. Shake in fear at her might.

+1 for the Numbers thing especially, it's an important point of Exalted in my opinion. Primordials were defeated by less powerful but more numerous Solars. Solars got defeated by less powerful but more numerous Dragon Blooded. And Dragon Blooded are careful, because now it is just them and less powerful but more numerous mortals...
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Cristol.GdMNov 29 '12 at 14:12

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It should be noted that the 2.5 Errata killed the combo system, making it far less likely for someone who has a perfect defense to be caught unable to use it, unless he's out of motes.
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DraupadiDec 7 '12 at 19:26

@Draupadi - I don't know if I should be amazed or depressed. I'm going to go download it now.
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CthosDec 7 '12 at 19:58

@Cthos They did increase the cost of perfects across the board and a whole lot of other tweaks. It's an improvement, but it's just a patchwork fix while we wait for 3e.
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DraupadiDec 7 '12 at 20:15

If the characters are unbeatable, force the players to make choices and decisions. This is similar to Undreren's comment (a lose-lose situation is one possibility), but I'd say concentrate more on forcing the players to achieve success. Make them do a logic puzzle that for whatever reason their characters can't do, force them to find clues and deduct the murderer, etc.

Alternatively, match the enemy to the player. If the player has perfect defense, the attacker may use traps or other tricks to bypass it. Someone excellent at solving mysteries may be confounded by someone who doesn't care about being found, and will happily be tracked to his lair where he attacks the players. A player with perfect attack could be faced with an NPC with perfect defense. Really, when the players can do anything in one area of the game, try to hang the plot on other parts if you can.

In some situations, look at taking their abilities away (I'd recommend being careful with this, and making sure to only do it temporarily, as players often spend a lot of time working towards a single ability and taking it away really gets on their nerves). Then hit them with something they could have stopped with their abilities. When they get their abilities back, they can go finish the situation.

Also, occasionally it's nice for players to be able to walk through a challenge. It helps them feel like they've improved and they can see how awesome their characters have become.

While generally this would be useful advice, it doesn't really apply to Exalted where being that powerful is the assumption. Bypassing perfect defenses is bad for several reasons and taking inherent abilities away is bad for similar reasons. Exalted assumes players start out epic and become even more epic as the game progresses.
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DraupadiNov 28 '12 at 18:31

You don't have to cripple the players to the point where they can't do anything, but I'd suggest removing the excess power that stops you as a GM from being able to use obstacles effectively. Also, in some situations, you might not need the character abilities as much.
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DakeyrasNov 28 '12 at 18:47

They are perfect, or at least near-perfect, in what they have chosen to do.

The drama from Exalted then comes in what happens when one of two events occurs:

Perfect runs into itself. Abyssals, Infernals other Solars etc. have the same claim to perfection, if somewhat tainted. When those two forces collide, there's a story to be told.

The perfection is that they succeed - not necessarily that they succeed in the way they want. Or which prevents them from being monsters. A Social Combat focused Solar may be able to impose her will on a city, but only by utterly rewriting their desires. A Dawn may claim rulership of Creation, but it will be after wading through a sea of blood. And the harder they have to fight opponents like Sidereals, the more they have to use the full extent of their power, and that's often something that should have some challenge attached to it. It's like asking the Hulk to hold your Faberge egg.

Exalted is very much a game where brute force is not supposed to be enough, and when brute force is not enough there are very few perfect effects to take into account. But here are a few pointers that could help challenge Exalted players.

Remember that the Solars are no longer a United force and are young. A sufficiently experienced sidereal can overpower a young Solar through brute force if he has to. Providing a combat challenge should not be an issue as long as you make your opponents strong enough to match your PC.

Bring problems that relate to the character's motivations and intimacies. See how you can threaten those. Do it right and you don't even need Exalted level characters to provide the threat. If your PCs have no good way to counter the plague that infected the village they care about, they'll need someone else's aid, who might just want them to perform a favor in return.

Push back. Have the NPCs of your world push back. The PCs are not the only Exalted, or even the only Exalted of their type. If your group encroaches upon the territory of another, the other might just encroach upon theirs. If your group is wasting peripheral essence a lot, call in the Wyld hunt.

Let them feel awesome some times. Let them win, let them have an easy victory just to remind them they're epic demigods with the right to rule the world. Sometimes just being epic can be just as fun as winning.

Always remember the hidden name of the game. Consequences. Exalted isn't about achieving your goals as much as it is about the consequences of your actions. It's the game where 'With great power comes great responsibility' is a default assumption. Responsibility wouldn't be great if you couldn't screw up big time by making the wrong choice. You can succeed at what you were trying to do but still regret it.

In my experience, there are two extremely common types of challenges in role playing games. These two categories are

challenges against a characters skill/ability,

and challenges against a characters morals/desires.

Let's look at the first one, the one you obviously have hid a road block with.

Challenges against a characters skill/ability

Roll Manipulation + Subterfuge...

When do we challenge the characters' skills and ability? The answer is pretty straight forward; every time we tell them to make a roll. Now that we have that out of the way, I would propose another, much more important question; why do we challenge the characters' skills and abilities?

The answer to this will probably vary from group to group, but I'm pretty sure that most people will agree that we make rolls to create suspense, or to allow the situation to take an unexpected turn. At least that is the underlying reason. Many rule books will simply say that we make rolls whenever the outcome is uncertain, but this is roughly the same.

In your game, the characters have "perfect skill", as you describe it, and they apparently always succeed at whatever they are good at. In this situation, ask yourself why you want to challenge them on their "specialty". What will it add to your game? If the player has a great time auto-succeeding, and no one else seems to mind, then go for it. But it won't add any kind of suspense or uncertainty to your game.

Whatever you do, don't "punish" the player, by making this ability pointless. He has spend some sort of resource becoming exceptionally good at something. Don't let him just sit there and regret he "wasted" points on it. Instead, use it as a possibility to make his character shine, make his character succeed where everyone else fails. The point of being good at something is to do it, after all. This will also make the character irreplaceable, which I personally believe every character should be, in any game.

Challenges against a characters morals/desires

"If you are not for me, then you are against me!" King Olaf shouts angrily at you. It seems, yet again, that you must choose sides...

Sometimes it is not about skill, but about choice. You can't fight on both sides of a war, as in the example above. This is a very efficient way to create drama, since every choice in a role playing game should be meaningful and therefore have repercussions.

A good choice can be your salvation, a bad one can be your downfall. Sometimes both choices are good, but conflict will greatly be magnified when all choices are bad.

When do we present characters with a hard choice? When we want to create drama, and when we want to let the players decide what comes next. In humble opinion, a hard choice is the ultimate storytelling aid. Have you ever seen a movie, where the hero doesn't have to make a hard choice? Wait, let me rephrase that; have you ever seen a good movie, where the hero doesn't have to make a hard choice?

Use these hard choices. Hard choices tell a better story than any single skill roll will ever do. Besides, making a player make a hard, meaningful choice, you put his character right there in the spotlight, and for a moment he is the most important person in the group.

Conclusion

If a character "cannot fail", then it is pointless to challenge him. But if he can't fail, then abuse it to tell great stories, where his perfection will advance the story in whatever way it must. But remember, for a story to be truly great, it must touch on something else than mere skill.

A characters skill is the players way to coerce the story in the way he wants it to go. Don't take it away from him, but remember to challenge his character on other skills as well.